Research Journal of Applied Sciences, Engineering and Technology 7(20): 4303-4312, 2014
ISSN: 2040-7459; e-ISSN: 2040-7467
© Maxwell Scientific Organization, 2014
Submitted: December 28, 2013
Accepted: January 16, 2014
Published: May 20, 2014
Sensor-less Field Oriented Control of Wind Turbine Driven Permanent Magnet
Synchronous Generator Using Flux Linkage and Back EMF Estimation Methods
1
Porselvi Thayumanavan, 2Ranganath Muthu and 3Jeyasudha Sankararaman
1
Department of EEE, Sri SaiRam Engineering College, Chennai, India
2
Department of EEE, SSN College of Engineering, Chennai, India
3
Department of EEE, Sri SaiRam Engineering College, India
Abstract: The study aims at the speed control of the wind turbine driven Permanent Magnet Synchronous Generator
(PMSG) by sensor-less Field Oriented Control (FOC) method. Two methods of sensor-less FOC are proposed to
control the speed and torque of the PMSG. The PMSG and the full-scale converter have an increasing market share
in variable speed Wind Energy Conversion System (WECS). When compared to the Induction Generators (IGs), the
PMSGs are smaller, easier to control and more efficient. In addition, the PMSG can operate at variable speeds, so
that the maximum power can be extracted even at low or medium wind speeds. Wind turbines generally employ
speed sensors or shaft position encoders to determine the speed and the position of the rotor. In order to reduce the
cost, maintenance and complexity concerned with the sensor, the sensor-less approach has been developed. This
study presents the sensor-less control techniques using the flux-linkage and the back EMF estimation methods.
Simulations for both the methods are carried out in MATLAB/SIMULINK. The simulated waveforms of the
reference speed, the measured speed, the reference torque, the measured torque and rotor position are shown for
both the methods.
Keywords: Back EMF estimation method, Field Oriented Control (FOC), flux linkage estimation method,
Permanent Magnet Synchronous Generator (PMSG), sensor-less control
INTRODUCTION
Variable-speed wind generation with the PMSG and
a full-scale power electronic converter is a promising
but not yet a very popular wind turbine concept. A
PMSG connected to a power electronic converter can
operate at low speeds, so a gearbox is not required.
Since the gearbox increases the weight, the losses, the
costs and demands more maintenance, a gearless
construction represents an efficient and a robust
solution, especially for offshore applications. Also, due
to the presence of the permanent magnet in the PMSG,
the DC excitation system can be eliminated, further
reducing the weight, the losses, the costs and the
maintenance requirements (Hsieh and Hsu, 2012; Qiao
et al., 2012). Thus, the efficiency of a PMSG based
wind energy system is higher than other variable-speed
WECS. In addition, a full-scale Insulated-Gate Bipolar
Transistor (IGBT) converter allows full controllability
of the system (Li et al., 2009, 2010). The generator-side
converter controls the generator speed to enhance the
wind power extraction. The control techniques for the
generator-side converter decouple the torque and flux
controls. Vector control or direct control technique is
used for this purpose. A rotor field oriented control is
applied to the generator-side converter to control the
generator speed and to obtain the maximum
electromagnetic torque with the minimum current. To
achieve this, the d-component of the stator currents is
forced to zero and the electromagnetic torque is
controlled only with the q-component of the current.
When compared to the direct control, vector control
achieves higher overall system efficiency, which is
mainly due to the lower current distortion and the
consequent lower joule losses (Freire et al., 2012).
Several techniques are available for the sensor-less
position and speed estimations. In Fan et al. (2010), a
digital phase-locked loop is used for the sensor-less
vector control of speed and position. This controls the
frequency of the output signal by a control signal that is
proportional to the difference between the output phase
of the system and the phase of the given signal. With
this obtained frequency characteristic, the motor speed
and the rotor position angle are measured. However, this
frequency control technique does not work well when
the motor runs at low speed. In Zhonggang et al. (2012),
a Robust Extended Kalman Filter (REKF) algorithm is
used for the sensor-less vector control. Although this
method provides less effect of gross error on the
estimation accuracy, the intensive calculations involved
are difficult to compute and time consuming.
High frequency signals injection method (Consoli
et al., 2001) is proven effective at low-speeds and even
at standstill for both the salient and non-salient pole
machines. However, the method requires additional
Corresponding Author: Porselvi Thayumanavan, Department of EEE, Sri SaiRam Engineering College, Chennai, India
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carrier signals, resulting in unnecessary losses, current
and torque distortions and acoustic noise.
A speed controller observer based on the model
reference adaptive control was proposed for the
Permanent Magnet Synchronous Motor (PMSM) in
Saikumar and Sivakumar (2011), Maiti et al. (2008) and
Kim et al. (1995). This controller requires two models,
which increase the complexity in the control and the
costs. In Yongchang et al. (2009), a comparison
between a Luenberger observer, a sliding mode observer
and an extended Kalman filter was made for the sensorless control of the induction machine. It was shown that
the first two methods are more suitable when compared
to the third method.
This study describes the sensor-less vector control
method of the PMSG. There are several methods of
sensor-less control of PMSG available. Two methods
are considered namely the flux linkage estimation
method and the back EMF estimation method.
Simulation is carried out in MATLAB/SIMULINK for
both the methods. A comparison based on the settling
time of speed and torque for the two methods is shown.
The simulated waveforms of the stator voltage, the
stator current, the reference speed, the measured speed,
the reference torque, the measured torque and the rotor
position are shown for both the methods for varying
reference speed and reference torque.
MATERIALS AND METHODS
Modeling of the PMSG: Equation (1) gives the
mathematical model of the PMSG derived from the
stator voltage equation:
v s = Rs i s +
d
Ψs
dt
dΨd
− ωe Ψq
dt
dΨq
vsq = Rs isq +
+ ωe Ψd
dt
(3)
where, ω e is the electrical speed in rad/s.
Equation (4) and (5) give the flux linkages in the dq reference frame:
Ψd = Ld isd + Ψm
3
Pem = ωe (Ψd isq − Ψqisd )
2
(4)
(6)
Equation (7) gives the relation between the
electrical and the mechanical speed:
ωe = pωm
(7)
where,
p = The number of pole pairs
ω m = The mechanical speed of the rotor
Hence, Eq. (8) gives the expression for the
electromagnetic torque:
P
3
Te = em = p(Ψd isq − Ψq isd )
ωm 2
(8)
By substituting the d-axis and the q-axis flux
linkages in Eq. (8) and by considering that the d-axis
and q-axis inductances for the surface mounted PMSG
are equal, the torque relation is finally derived and
given by Eq. (9):
3
Te = p(Ψmisq )
2
(2)
(5)
where, ψ d and ψ q are the d-axis and q-axis flux
linkages, respectively, L d and L q are the d-axis and the
q-axis inductances, respectively and ψ m is the
permanent magnet flux linkage.
Equation (6) gives the electromagnetic power from
which the electromagnetic torque derived:
(1)
where, v s , i s and Ψs are the space vectors of the stator
voltages, the stator currents and the flux linkages,
respectively.
Equation (2) and (3) give the voltage equations in
the d-q reference frame with the d-axis coinciding with
the permanent magnet pole axis:
vsd = Rs isd +
Ψq = Lq isq
(9)
Equation (10) shows the general mechanical
equation of the machine:
d
Te = TL + Bωm + Td + J ωm
dt
(10)
where,
T L = The load torque
J = The moment of inertia
B = The viscous frictional coefficient
Field oriented control: Field Oriented Control (FOC)
is a vector control technique, which controls the torque
indirectly by controlling the stator currents. The
constant torque angle control is used in this study. In
this method, the torque angle is kept at 90°. The d-axis
current component is set to zero and therefore the
stator current has only the q-axis component. Since the
torque angle and the permanent magnet flux are
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Res. J. Appl. Sci. Eng. Technol., 7(20): 4303-4312, 2014
Fig. 1: Field oriented control of the PMSG with the sensor
constant, the torque depends only on the q-axis stator
current.
As the current control is performed on the rotor
reference frame, a transformation of coordinates is
required to obtain the reference stator currents. FOC
eliminates current cross coupling between the d and q
axes components, which requires feed-forward
compensation. In the FOC, the permanent magnet flux
linkage is aligned along the d-axis.
Figure 1 gives the block diagram of the FOC of the
PMSG with the sensor. In this control, the speed is
sensed and compared with the reference speed. The
error in speed is processed in the PI controller to obtain
the reference q-axis current. The reference d-axis
current is set to zero. The stator currents from the
PMSG are transformed to the d-q reference frame and
compared with the reference d-q currents.
For decoupling purposes, a feed-forward loop is
used. This includes the components I and II, which are
given by:
Component I: ωe Ψq = ωeisq Lq
Component II: ωe Ψ = ωei L + Ψm
d
sd d
V dc and V αβ are given to space vector modulation
block to produce the gate signals for the converter
switches.
q-axis current controller design: Figure 2 shows the
block diagram for the design of the q-axis current
controller. The various blocks are the PI block, the
delay introduced by the PI, the delay introduced by the
inverter, the plant that is the stator block and the delay
Fig. 2: Block diagram for the design of the q-axis current
controller
introduced due the digital to analog conversion, which
is taken to be equal to half of the delay introduced by
the PI.
Equation (11) gives the transfer function of the qaxis current controller:
1
Gq (s) = K pq (1 +
)
sTiq
(11)
where,
K pq = The proportional gain of the q-axis current
controller
T iq = The integral time constant of the q-axis current
controller
d -axis current controller design: The d-axis current
controller is implemented in the same way as the qaxis current controller except that the L q is replaced
by L d . Equation (12) gives the transfer function of the
d-axis current controller:
1
Gd (s) = K pd (1 +
)
sTid
(12)
where,
K pd = The proportional gain of the d-axis current
controller
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Res. J. Appl. Sci. Eng. Technol., 7(20): 4303-4312, 2014
where, k is the present sampling interval and k-1 is the
previous sampling interval. The currents i α and i β (i.e.,
the stator currents in the stationary reference frame)
are obtained by measuring the a, the b and the c stator
phase currents.
Step 2: Stator current estimation: The stator currents
are estimated by the flux linkages estimated in
step 1 and the predicted rotor position in step
5. The stator currents are then estimated using
Eq. (16) and (17):
Fig. 3: Design of the speed controller
T id = The integral time constant of the d-axis current
controller
q-axis speed controller design: Figure 3 shows the
block diagram for the design of the speed controller,
where, τ iq = L q /R s , p is the number of pole pairs, T f is
the filter time constant used only when an encoder
measures the speed.
Equation (13) gives the transfer function of the PI
speed controller:
Gω ( s ) = K pω (1 +
1
)
sTiω
Ψα = −∆L sin(2θ r )iβ + ( L − ∆L cos(2θ r ))iα + Ψm cosθ r
(16)
Ψβ = − ∆L sin( 2θ r )iα + ( L + ∆L cos(2θ r ))iβ + Ψm sin θ r
where, L =
Ld + Lq
2
(17)
and ∆L =
Lq − Ld
.
2
Figure 5 shows the various steps involved in the
estimation of rotor position.
(13)
where,
K pω = The proportional gain of the speed controller
T iω = The integral time constant of the speed controller
Sensor-less control: Using a sensor to encode the
speed has several drawbacks like, increased cost, bigger
size and lower reliability of the system. This study,
therefore, presents the sensor-less control methods
using the flux linkage and the back-EMF estimation
methods.
Figure 4 shows the block diagram of the FOC of
the PMSG without the sensor. In this control, the stator
currents from the PMSG are taken and transformed to
the α-β reference frame. The currents in the α-β
reference frame are given to the position and speed
estimation blocks.
Flux linkage estimation method: This method is used
for estimating the position of the rotor. The rotor
position estimation is based on the estimation of the
flux linkages. The initial rotor position is found from
the flux linkage using the inductances and the stator
currents (Lukko, 2000). Sensor-less control method is
implemented in five steps:
Step 1: Estimation of the stator flux linkages: Phase
currents and voltages are assumed to be
measured at a fixed sample time T s . The stator
flux linkages are given in Eq. (14) and (15):
Ψα (k ) = Ts [v(k −1) − Rs iα (k )] + Ψα (k − 1)
(14)
Ψβ (k ) = Ts [v(k − 1) − Rs iβ (k )] + Ψβ (k − 1)
(15)
Step 3: Position correction: In this step, the rotor
position predicted in step 5 is corrected with
the errors of the stator currents. The errors of
the current are obtained from the difference
between the measured and estimated currents.
Equation (18) and (19) give the errors of the
current in the d and q axes reference frames,
respectively:
∆iq = ∆iβ cos(θ p ) − ∆iα sin(θ p )
(18)
∆id = ∆iβ sin(θ p ) + ∆iα cos(θ p )
(19)
The corrected position is obtained by adding the
position error to the predicted position, as given in
Eq. (20):
θ r (k ) = θ p (k ) + ∆θ (k )
(20)
where, Ө r and Ө p are the corrected and the predicted
rotor angles respectively.
Step 4: Flux linkage updating: In this step, the
fluxes are recalculated using the
corrected rotor position and the measured
stator currents. Equation (21) and (22)
express the fluxes in discrete time:
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Ψα (k ) = [ L − ∆L cos(2θ r (k ))]iα (k ) − ∆L sin( 2θ r (k ))iβ (k ) +
Ψm cos(θ r (k ))
(21)
Res. J. Appl. Sci. Eng. Technol., 7(20): 4303-4312, 2014
Fig. 4: Field oriented control of the PMSG without the sensor
same position as that of the back EMF, as shown in
Fig. 6.
The position of the back EMF space vector is
determined using Eq. (24):
es
θ r = tan −1 sd
e q
(24)
In order to have a simpler model, the Clarke’s
transformation is used. Equation (25) gives the relation
between the abc and the α-β reference frames:
vα

vβ
Ψβ (k ) = [ L + ∆L cos(2θ r (k ))]iβ (k ) − ∆L sin(2θ r (k ))iα (k ) +
(25)
(22)
Step 5: Position prediction: Considering position to be
a second-order polynomial, the position
prediction can be expressed by Eq. (23):
θ p = et 2 + ft + g

1 1  v 
1− −
a
2 2   
2 
=
vb 
3
3
3  
−
0

2
2  vc 

By knowing the voltages of the stator in the α-ß
reference frame, the stator angle is calculated as by
Eq. (26):
Fig. 5: Steps for the estimation of rotor position
Ψm sin(θ r (k ))



(23)
where, e, f, g are constants (Chandana Perera, 2002).
Back-EMF estimation method: The permanent
magnet flux is aligned with the d-axis, while the
induced voltage of the permanent magnet flux i.e., the
back-EMF is along the q-axis. This back EMF can be
used to calculate the rotor position. The rotor is in the
θ v = tan −1
v
β
vα
(26)
where, v α and v β are the stator voltages in the α-ß
reference frame.
Now, the variables in the α-β reference frame are
transformed into a new reference frame of δ-φ, which is
shown in Fig. 7.
Equation (27) gives the transformation matrix that
converts the α-β variables to the δ-φ variables:
4307
vδ  cos θ v sin θ v  vα 
 =
 v 
vϕ  − sin θ v cos θ v   β 
(27)
Res. J. Appl. Sci. Eng. Technol., 7(20): 4303-4312, 2014
where,
= The rotational speed of i s
ωi
e δ and e φ =
Back EMFS of the stator in δ-φ
reference frame, respectively
They can be expressed by Eq. (30) and (31):
eδ = ωeλm sin θ n
(30)
eϕ = ωeλm cosθ n
(31)
where,
ω e = The rotor electrical speed
λ m = The permanent magnet flux linkage
Ө n = The estimated rotor angle in δ-φ reference frame
Fig. 6: Space vector representation of the back EMF
At steady state, the currents i δ and i φ are constant,
resulting in the derivative term of the Eq. (28) and (29)
becoming zero. Assuming ideal conditions, the rotor
position in the δ-φ reference frame is determined from
Eq. (30) and (31) and is expressed by Eq. (32):
v − Rs iδ + ωi Ls iδ
θ n = tan −1 δ
vϕ − Rs iδ − ωi Ls iϕ
(32)
Equation (33) gives the estimated rotor position:
Fig. 7: Relationship between α-β and δ-φ frame
Now, the stator voltage is aligned with the δ axis
with the v φ component equal to zero. The voltage
equations of the PMSG in the δ-φ co-ordinate system
are given by Eq. (28) and (29):
di
vδ = Rs iδ + Ls δ − ωi Ls iδ + eδ
dt
(28)
diϕ
vφ = Rs iϕ + Ls
+ ωi Ls iϕ + eϕ
dt
(29)
θ = θv −θ n
(33)
RESULTS AND DISCUSSION
The system is simulated in MATLAB/SIMULINK
for the sensor-less field oriented control with the flux
linkage and back-EMF estimation methods. The initial
reference speed and torque are 700 rpm and -9 Nm,
respectively. Then the reference speed alone is changed
to 1000 rpm at 2 sec with the same torque. At 4 sec, the
reference torque is changed to -12 Nm, with the speed
reference at 1000 rpm. Figure 8 and 9, respectively
Fig. 8: The reference and measured speeds of the PMSG for the flux linkage estimation method
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Fig. 9: The reference and measured torques of the PMSG for the flux linkage estimation method
Fig. 10: Measured and estimated rotor positions for the flux linkage estimation method
show the reference and measured speeds and the
reference and measured torques for the flux linkage
estimation method. Figure 10 shows the measured and
estimated rotor position for the flux linkage estimation
method.
Figure 11 and 12, respectively show the reference
and measured speeds and the reference and measured
torques for the back-EMF estimation method.
From the Fig. 8 and 11, it is found that the speed
follows the reference speed. Initially, when the
reference speed was set at 700 rpm, the PMSG follows
the reference speed of 700 rpm. When the reference
speed changes to 1000 rpm at t = 2 sec, the speed of the
PMSG also changes and reaches the reference speed
within 0.028 sec for the flux linkage and the back-EMF
methods. There is a little oscillation in speed at t = 4 sec
which is due to the change in the reference torque,
which also damps out within 0.01 sec for the flux
linkage method. However, some oscillations exist in
back-EMF estimation method, which damps out within
0.015 sec. It is found from the Fig. 11 that, there are
some oscillations speed in the system with the change
in the reference speed and torque for the back EMF
estimation method.
From Fig. 9 and 12, it is found that the torque
follows the reference torque of -9 Nm up to t = 4 sec.
The torque oscillates at 2 sec due to the change in the
reference speed. The oscillation is damped out in 0.02
sec for the flux linkage method and in 0.025 sec for the
back EMF method. When the torque reference is
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Res. J. Appl. Sci. Eng. Technol., 7(20): 4303-4312, 2014
Fig. 11: Reference and measured speeds of the PMSG for the back-EMF estimation method
Fig. 12: Reference and measured torque of PMSG for the back EMF estimation method
Fig. 13: The measured and the estimated rotor position for the back-EMF estimation method
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Table 1: Comparison of the flux linkage and back EMF methods
Settling time for speed (sec)
----------------------------------------------------------Due to change in
Due to change in
speed reference
torque reference
Method
Flux linkage estimation method
0.028
0.010
Back EMF estimation method
0.028
0.015
changed to -12 Nm at t = 4 sec, it is seen that the torque
of the PMSG also changes and reaches the reference
torque within 0.005 sec for the flux linkage method and
within 0.01 sec for the back-EMF method.
Figure 13 shows the measured and estimated rotor
positions for the back-EMF estimation method.
Table 1 shows the comparison of the flux linkage
and the back EMF estimation methods based on the
settling time of speed and torque for change in speed
and torque.
It is found from the Fig. 8, 9, 11 and 12 and the
Table 1, that the response for the flux linkage method is
faster than the back-EMF method. In addition, it is
evident from the waveforms that, the presence of
oscillations is more in the back-EMF method.
CONCLUSION
The PMSG is modelled in the d-q reference frame
with the d-axis aligned with the permanent magnet axis.
The PMSG is controlled with a sensor-less field
oriented control for varying reference speeds and
torques. The sensor-less tracking of the position and the
speed of the PMSG is carried out using the flux linkage
estimation method and the back-EMF estimation
methods. The two control methods are simulated using
the MATLAB/SIMULINK. The flux linkage estimation
method shows a faster response to the change in
reference speed and torque. This improves the
robustness and the effectiveness of the system. In spite
of the many advantages, this algorithm uses sampled
data from the previous time instant, which introduces
certain time delay in the system and presents integration
drift problems. The back-EMF method presents certain
oscillations in the system with the change in the
reference speed and torque and has sensitivity problems
with parameter changes. The main drawback of the
back-EMF estimation method is the estimation of the
position of the rotor at zero speed or low speed ranges,
because the back EMF becomes zero and thus the
position estimation is not possible. At low speeds, the
back-EMF is very small which leads to a large error in
the estimation. From the simulated results, it is
observed that better control is achieved with the flux
linkage estimation method as compared to the backEMF estimation method.
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Settling time for torque (sec)
----------------------------------------------------Due to change in
Due to change in
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